Abstract
We present a general method to disprove generalized Brunn–Minkowski inequalities. We initially developed this method in [14] in the particular case of the sub-Riemannian Heisenberg group in order to prove that this space does not satisfy a curvature-dimension condition in the sense of Lott–Villani and Sturm.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1216.28007
MathSciNet: MR2648260
Digital Object Identifier: 10.2969/aspm/05710189
Subjects:
Primary:
28A75
,
53C17
Keywords:
Brunn–Minkowski inequality
,
curvature-dimension
,
Grušin plane
,
Heisenberg group
,
Optimal transport
Rights: Copyright © 2010 Mathematical Society of Japan
